Final answer:
The total cost function for producing tote bags is C(b) = 3b + $12,000. Using this function, the cost for producing 200 tote bags is $12,600, and the cost for producing 625 tote bags is $13,875. The provided answer choices do not include these correct values, indicating a possible error.
Step-by-step explanation:
To determine the total cost function for producing tote bags, we must add the variable costs (which depend on the number of bags produced) to the fixed costs (which are constant regardless of production).
Given that the fixed costs are $12,000 and the variable costs are $3 per tote bag, we can write the total cost function as C(b) = 3b + $12,000, which represents the total cost of producing b tote bags.
To find C(200), we simply substitute b with 200 in our total cost function: C(200) = 3(200) + $12,000 = $600 + $12,000 = $12,600. This is not one of the options provided in the question, so it is possible that there has been an error in the question or answer choices.
For the cost of producing 625 tote bags, we substitute b with 625 in the total cost function: C(625) = 3(625) + $12,000 = $1,875 + $12,000 = $13,875. Again, this correct answer is not listed in the options.